Question: Simplify to lowest terms. $\dfrac{30}{24}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 30 and 24? $30 = 2\cdot3\cdot5$ $24 = 2\cdot2\cdot2\cdot3$ $\mbox{GCD}(30, 24) = 2\cdot3 = 6$ $\dfrac{30}{24} = \dfrac{5 \cdot 6}{ 4\cdot 6}$ $\hphantom{\dfrac{30}{24}} = \dfrac{5}{4} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{30}{24}} = \dfrac{5}{4} \cdot 1$ $\hphantom{\dfrac{30}{24}} = \dfrac{5}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{30}{24}= \dfrac{2\cdot15}{2\cdot12}= \dfrac{2\cdot 3\cdot5}{2\cdot 3\cdot4}= \dfrac{5}{4}$